Absorption bound of a locally resonant element in a unidimensional scattering problem
Résumé
We consider the scattering properties of a locally resonant element either in series or in parallel of a waveguide resulting in a unidimensional problem. At the downstream side of the waveguide, an arbitrary passive outlet boundary is accounted for by introducing an impedance boundary condition. The goal is to suppress both the reflected and the transmitted waves by the locally resonant element. It is shown that the absorption coefficient of the system has a frequency-dependent upper bound, which is in general less than one and depends on the impedance of the outlet. The analytical prediction of the maximum absorption is validated against experiment results obtained with specifically designed samples, which work for either a single frequency or a broadband frequency range.